40 research outputs found
Topological Structure of the QCD Vacuum Revealed by Overlap Fermions
Overlap fermions preserve a remnant of chiral symmetry on the lattice. They
are a powerful tool to investigate the topological structure of the vacuum of
Yang-Mills theory and full QCD. Recent results concerning the localization of
topological charge and the localization and local chirality of the overlap
eigenmodes are reported. The charge distribution is radically different, if a
spectral cut-off for the Dirac eigenmodes is applied. The density q(x) is
changing from the scale-a charge density (with full lattice resolution) to the
ultraviolet filtered charge density. The scale-a density, computed on the Linux
cluster of LRZ, has a singular, sign-coherent global structure of co-dimension
1 first described by the Kentucky group. We stress, however, the cluster
properties of the UV filtered topological density resembling the instanton
picture. The spectral cut-off can be mapped to a bosonic smearing procedure.
The UV filtered field strength reveals a high degree of (anti)selfduality at
"hot spots" of the action. The fermionic eigenmodes show a high degree of local
chirality. The lowest modes are seen to be localized in low-dimensional
space-time regions.Comment: 13 pages, 11 figures, accepted to appear in the Proceedings of "HLRB,
KONWIHR and Linux-Cluster: Review, Results and Future Projects Workshop",
Leibniz Rechenzentrum Munich, December 200
Quark zero modes in intersecting center vortex gauge fields
The zero modes of the Dirac operator in the background of center vortex gauge
field configurations in and are examined. If the net flux in D=2
is larger than 1 we obtain normalizable zero modes which are mainly localized
at the vortices. In D=4 quasi-normalizable zero modes exist for intersecting
flat vortex sheets with the Pontryagin index equal to 2. These zero modes are
mainly localized at the vortex intersection points, which carry a topological
charge of . To circumvent the problem of normalizability the
space-time manifold is chosen to be the (compact) torus \T^2 and \T^4,
respectively. According to the index theorem there are normalizable zero modes
on \T^2 if the net flux is non-zero. These zero modes are localized at the
vortices. On \T^4 zero modes exist for a non-vanishing Pontryagin index. As
in these zero modes are localized at the vortex intersection points.Comment: 20 pages, 4 figures, LaTeX2e, references added, treatment of ideal
vortices on the torus shortene
Divergent IR gluon propagator from Ward-Slavnov-Taylor identities?
We exploit the Ward-Slavnov-Taylor identity relating the 3-gluons to the
ghost-gluon vertices to conclude either that the ghost dressing function is
finite and non vanishing at zero momentum while the gluon propagator diverges
(although it may do so weakly enough not to be in contradiction with current
lattice data) or that the 3-gluons vertex is non-regular when one momentum goes
to zero. We stress that those results should be kept in mind when one studies
the Infrared properties of the ghost and gluon propagators, for example by
means of Dyson-Schwinger equations.Comment: 6 pages, bibte
Indirect determination of the Kugo-Ojima function from lattice data
We study the structure and non-perturbative properties of a special Green's
function, u(q), whose infrared behavior has traditionally served as the
standard criterion for the realization of the Kugo-Ojima confinement mechanism.
It turns out that, in the Landau gauge, u(q) can be determined from a dynamical
equation, whose main ingredients are the gluon propagator and the ghost
dressing function, integrated over all physical momenta. Using as input for
these two (infrared finite) quantities recent lattice data, we obtain an
indirect determination of u(q). The results of this mixed procedure are in
excellent agreement with those found previously on the lattice, through a
direct simulation of this function. Most importantly, in the deep infrared the
function deviates considerably from the value associated with the realization
of the aforementioned confinement scenario. In addition, the dependence of
u(q), and especially of its value at the origin, on the renormalization point
is clearly established. Some of the possible implications of these results are
briefly discussed.Comment: 25 pages, 10 figures; v2: typos corrected, expanded version that
matches the published articl
Non-Commutativity of the Zero Chemical Potential Limit and the Thermodynamic Limit in Finite Density Systems
Monte Carlo simulations of finite density systems are often plagued by the
complex action problem. We point out that there exists certain
non-commutativity in the zero chemical potential limit and the thermodynamic
limit when one tries to study such systems by reweighting techniques. This is
demonstrated by explicit calculations in a Random Matrix Theory, which is
thought to be a simple qualitative model for finite density QCD. The
factorization method allows us to understand how the non-commutativity, which
appears at the intermediate steps, cancels in the end results for physical
observables.Comment: 7 pages, 9 figure
Calibration of Smearing and Cooling Algorithms in SU(3)-Color Gauge Theory
The action and topological charge are used to determine the relative rates of
standard cooling and smearing algorithms in pure SU(3)-color gauge theory. We
consider representative gauge field configurations on lattices
at and lattices at . We find the
relative rate of variation in the action and topological charge under various
algorithms may be succinctly described in terms of simple formulae. The results
are in accord with recent suggestions from fat-link perturbation theory.Comment: RevTeX, 25 pages, 22 figures, full resolution jpeg version of Fig. 22
can be obtained from
http://www.physics.adelaide.edu.au/cssm/papers_etc/SmearingComp.jp
Chiral phase boundary of QCD at finite temperature
We analyze the approach to chiral symmetry breaking in QCD at finite
temperature, using the functional renormalization group. We compute the running
gauge coupling in QCD for all temperatures and scales within a simple truncated
renormalization flow. At finite temperature, the coupling is governed by a
fixed point of the 3-dimensional theory for scales smaller than the
corresponding temperature. Chiral symmetry breaking is approached if the
running coupling drives the quark sector to criticality. We quantitatively
determine the phase boundary in the plane of temperature and number of flavors
and find good agreement with lattice results. As a generic and testable
prediction, we observe that our underlying IR fixed-point scenario leaves its
imprint in the shape of the phase boundary near the critical flavor number:
here, the scaling of the critical temperature is determined by the
zero-temperature IR critical exponent of the running coupling.Comment: 39 pages, 8 figure
Universality, vortices and confinement: modified SO(3) lattice gauge theory at non-zero temperature
We investigate the adjoint SU(2) lattice gauge theory in 3+1 dimensions with
the Wilson plaquette action modified by a Z(2) monopole suppression term. For
the zero-twist sector we report indications for the existence of a finite
temperature effect decoupled from the unphysical bulk transitions.Comment: 17 pages, 10 figures. Some figures and text added. To appear on Phys.
Rev.
Infrared Behavior of Three-Point Functions in Landau Gauge Yang-Mills Theory
Analytic solutions for the three-gluon and ghost-gluon vertices in Landau
gauge Yang-Mills theory at low momenta are presented in terms of hypergeometric
series. They do not only show the expected scaling behavior but also additional
kinematic divergences when only one momentum goes to zero. These singularities,
which have also been proposed previously, induce a strong dependence on the
kinematics in many dressing functions. The results are generalized to two and
three dimensions and a range of values for the ghost propagator's infrared
exponent kappa.Comment: 21 pages, 29 figures; numerical data of the infrared dressing
functions can be obtained from the authors v2: a few minor changes,
corresponds to version appearing in EPJ
Topological susceptibility with the improved Asqtad action
As a test of the chiral properties of the improved Asqtad (staggered fermion)
action, we have been measuring the topological susceptibility as a function of
quark masses for 2 + 1 dynamical flavors. We report preliminary results, which
show reasonable agreement with leading order chiral perturbation theory for
lattice spacing less than 0.1 fm. The total topological charge, however, shows
strong persistence over Monte Carlo time.Comment: Lattice2002(algor